Upload
others
View
11
Download
0
Embed Size (px)
Citation preview
A LiDAR Error Model for Cooperative Driving SimulationsPresenter: Rahul Bhadani, PhD Student, The University of Arizona
Authors: Michele Segata, Renato Lo Cigno, Rahul Bhadani, Matthew Bunting, Jonathan Sprinkle
2018 IEEE Vehicular Networking Conference (VNC) December 5–7, 2018, Taipei, Taiwan
Agenda
Motivation
Dataset description
Trace Analysis
Cooperative driving
Simulation
Motivation
Simulation Field Operation Tests
Huge Costs
Negligible approximation of physical processes
Unlimited use cases
Safety
Repeatability
Scalability issue
Repeatability issue
Real Vehicle/Hardware
Application development for connected and autonomous vehicles
Lack of sensor characterization
Lane detection
Motivation
Importance of sensor characterization for cooperative driving
Distance measurement
Emergency brakingFaul
ty mea
surem
ent
Stochastic error
modeling
Motivation
Key contribution of the presented research
Analysis of real-world LiDAR traces to understand the
underlying model
Development of a stochastic error model, capable of reproducing
measurement errors
Impact of stochastic error on control algorithm
using PLEXE simulation
Dataset description
Ring road experiment with 22 cars to demonstrate capability of autonomous vehicle to reduce traffic congestions in urban stop-and-go traffic
AV used LiDAR to feed distance to the velocity controller
A bird’s eye-view of ring road experiment
Schematic of LiDAR scanning
Relevant publication to the experiment: Stern, R. E., Cui, S., Delle Monache, M. L., Bhadani, R., Bunting, M., Churchill, M., ... & Seibold, B. (2018). Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments. Transportation Research Part C: Emerging Technologies, 89, 205-221.
Experiment Methodology
Determine minimum distance point along the trajectory to estimate headway distance
Kalman Filter to remove noise before feeding to the controller
Dataset description
Presented work builds stochastic error model on the top of filtered, yet imperfect
sampled data
Used 5th order butterworth low pass filter to clean the trace: used as
ground truth after compensating delay
Dataset description
Available dataset
https://doi.org/10.15695/vudata.cee.1
Exponential shot noise: exponential decay is caused by Kalman Filter
Trace Analysis
Analysis of LiDAR data
Trace Analysis
A closer look at traces for shot-errors
Error in shot-free portion: due to correlated stochastic process
Shot-noise error: random, modeled by Poisson process
𝝐[k] = 𝝐c[k] + 𝝐s[k]
Trace Analysis
Estimation of correlated noise 𝝐c[k]
Assumption: correlated error to be of the first order autoregressive form:
𝝐c[k] = ρ𝝐c[k-1] + Nc[k]
Nc: the innovation process of error of zero meanρ = Correlation coefficient by computing autocorrelation with a lag of 1 sample on shot-free portions of the error
Residual in innovation process
Trace Analysis
Estimation of correlated noise 𝝐c[k]
For parameter estimation of the model, we used maximum likelihood
estimation
Nc process: generated by multiplying samples drawn from fitted
distribution by B・2 - 1, B is bernoulli distribution with p =0.5
Distribution with highest likelihood was found to be pareto distribution
with 𝝁= 0 and 𝝈 = 0.0036
Hence, Autoregressive process Nc is:
Trace Analysis
Estimation of shot noise 𝝐s[k]
Limited number of shots in the dataset: no proper fittingWe focus on estimating nature of shot noise instead.
We estimate:
● Interarrival time of homogeneous Poisson process
● Exponential decay parameter● Amplitude of shots
From the dataset, we have 52 samples of shot noise over 686s, which gives λ = 0.0758.
LiDAR has sampling rate of 75 Hz, hence:
λ = Average number of occurrencesν = sampling time
On an average, we have one shots per 1000 samples.
● 3-points strategy for estimation of shot noise: sk-1, sk , ss+1 to compute decay parameter 𝜏.
Trace Analysis
Estimation of shot noise 𝝐s[k]
Let’s look exponential decay:
No is the amplitude of the shot noise.Solving for No:
We take the average of 𝜏, which is 23.576.
● Computing sk - sk-1 for amplitude, but not this straightforward during burst of shot noise.
● Burst has time-varying correlated noise, but we don’t have enough information to calculate value of correlated noise during bursts.
● Hence, we are limited to isolated shot noise and at the beginning of the burst noise.
● More details in the paper, page 5
Trace Analysis
Estimation of shot noise 𝝐s[k]
Estimating amplitude of the shot noise ● From dataset, average amplitude of shot noise is 4.364
● Not enough to draw conclusion on distribution of amplitude of shot noise: we make strong assumption that amplitude has exponential distribution with mean of 4.364.
● Putting together:
E is random number generator for Erlang-distribution based shot characteristic from dataset.
Detailed discussion in the paper
● Estimation is based on sampling rate of 75 Hz, which is operating frequency of LiDAR
● Synthetically generated data obtained from empirical distribution has smaller error, most probably because of low order of autoregressive process.
Trace Analysis
Final words on empirical distribution of noise
Synthetically generated trace from empirical distribution
Cooperative driving
Simulation
Impact of sensor noise on cooperative driving: a simulation study
PLEXE: A cooperative driving simulator
Realistic vehicular networking models
Realistic vehicle dynamics
Platoon control algorithms
No Error models: assumes error-free measurement
We used error modeled developed in the presented work to study cooperative driving via simulation under noisy conditions.
Simulation setup
Setup 1: 8 cars with the leader following a constant velocity profile
Cooperative driving
Simulation
Steady state distanceSetup 2: 8 cars with the leader following a
sinusoidal velocity profile
3 control algorithm considered: standard adaptive cruise control, PATH’s cooperative
ACC, Ploeg’s ACC
Implemented as acceleration control:
Steady state distance:
ACC: constant time-headway spacing policyPATH’s ACC: constant distance spacing policyPloeg’s ACC: constant time-headway spacing policy with string stability at small headway
Rate:Control system at 100Hz, LiDAR at 75Hz
Simulation with constant velocity profile: ACC
Notice positive acceleration spikes which may have been caused by LiDAR shot-errors
LiDAR error introduces perturbation in the system which is amplified by following vehicles. Sinusoidal amplification near shot errors.
Impact of incorporating error model on control dynamics of non-cooperative ACC
Simulation with constant velocity profile: Cooperative ACC
Incorporating LiDAR error model introduces some disturbance and causes inter-vehicle distance to float around steady-state value. As result these errors do not control system to stabilize distance value.
Simulation with sinusoidal velocity profile: Cooperative ACC
PATH’s CACC Ploeg’s CACC
Discussion about future work
● Empirical model of error derived from LiDAR traces helped spotting instabilities in control systems for cooperative vehicular network.
● Although, we made some strong assumptions about nature of error.● Lack of ground truth data was a major problem.● Analysis was based on Kalman filtered trace which have additional delay due
to filtering.● Due to assumption of first order autoregressive model, dataset still shows
some residual correlation.● Relative speed is assumed to be perfectly known which is not true in reality
and may exhibit high frequency noise.● Shot-noise were assumed to be independent which may lead to overestimation
of actual distance.
In upcoming work, we are going to relax our assumptions to come up with generalized error model.
Lab page: http://csl.arizona.edu
Authors’ webpage:http://csl.arizona.edu/~rahulbhadanihttps://ans.disi.unitn.it/~segata/https://disi.unitn.it/locigno/http://csl.arizona.edu/~sprinkjmhttp://csl.arizona.edu/~mosfet
Contact: [email protected]